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c(0)+(c(1))/(2)+(c(2))/(3)+...+(c(n))/(c...

c_(0)+(c_(1))/(2)+(c_(2))/(3)+...+(c_(n))/(c_(n+1))=(2^(n+1)-1)/(n+1)

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Prove that (i) C_(1)+2C_(2)+3C_(3)+……+nC_(n)=n.2^(n-1) (ii) C_(0)+(C_(1)/(2)+(C_(2))/(3)+….+(C_(n))/(n+1)=(2^(n+1)-1)/(n+1)

Prove that (i) C_(1)+2C_(2)+3C_(3)+……+nC_(n)=n.2^(n+1) (ii) C_(0)+(C_(1)/(2)+(C_(2))/(3)+….+(C_(n))/(n+1)=(2^(n+1)-1)/(n+1)

If (1+x)^(n)=C_(0)+C_(1)x+C_(2)x^(2)+.....+C_(n)x^(n) then show : (C_(0))/(1)+(C_(1))/(2)+(C_(2))/(3)+......+(C_(n))/(n+1)=(2^(n+1)-1)/(n+1)

If (1+x)^(n)=C_(0)+C_(1)x+C_(2)x^(2)+…+C_(n)x^(n) , show that, (C_(0))/(1)+(C_(1))/(2)+(C_(2))/(3)+…+(C_(n))/(n+1)=(2^(n+1))/(n+1)

C_(0)-(C_(1))/(2)+(C_(2))/(3)-......+(-1)^(n)(C_(n))/(n+1)=(1)/(n+1)

Prove the following: C_(0)-(C_(1))/(2)+(C_(2))/(3) - …+(-1)^(n)(C_(n))/(n+1)=(1)/(n+1)

If (1 + x)^(n) = C_(0) + C_(1) x + C_(2) x^(2) + C_(3) x^(3) + … + C_(n) x^(n) , prove that C_(0) - (C_(1))/(2) + (C_(2))/(3) -…+ (-1)^(n) (C_(n))/(n+1) = (1)/(n+1) .

If (1 + x)^(n) = C_(0) + C_(1) x + C_(2) x^(2) + C_(3) x^(3) + … + C_(n) x^(n) , prove that C_(0) - (C_(1))/(2) + (C_(2))/(3) -…+ (-1)^(n) (C_(n))/(n+1) = (1)/(n+1) .

If (1+x)^(n)=C_(0)+C_(1)x+C_(2)x^(2)+.....+C_(n)x^(n) then show : (C_(0))/(1)-(C_(1))/(2)+(C_(2))/(3)-......+(-1)^(n).(C_(n))/(n+1)=(1)/(n+1)